I need a cable to connect the GPU to the extender and an other one from the extender to the monitor. I have already tried a DisplayPort to HDMI adapter, but it did not work with the required resolution. Does a cable for my needs exist? Is it going to work with an other display, what has a native resolution of 2560x1600?

So with a "passive" cable it is not possible. Do you offer an "active" solution which converts the stream? Or do I have to buy a new DisplayPort or Dual link DVI capable transmitter? Which one is the most affordable?